Question

is $4\frac{1}{7}$ a rational number?

Explanation:

Step1: Recall the definition of rational numbers

A rational number is a number that can be expressed as $\frac{p}{q}$, where $p$ and $q$ are integers and $q
eq0$.

Step2: Analyze the number $4\frac{1}{7}$

First, convert the mixed number $4\frac{1}{7}$ to an improper fraction. The formula for converting a mixed number $a\frac{b}{c}$ to an improper fraction is $\frac{a\times c + b}{c}$. So for $4\frac{1}{7}$, we have $a = 4$, $b = 1$, $c = 7$. Then $4\frac{1}{7}=\frac{4\times7 + 1}{7}=\frac{28 + 1}{7}=\frac{29}{7}$. Here, $p = 29$ (an integer) and $q = 7$ (a non - zero integer). Since $4\frac{1}{7}$ can be written in the form $\frac{p}{q}$ with $p\in\mathbb{Z}$ and $q\in\mathbb{Z},q
eq0$, it satisfies the definition of a rational number.

Answer:

Yes, $4\frac{1}{7}$ is a rational number.